Asymptotic behavior of positive solutions to the Hénon-Lane-Emden system

In this paper, we study the asymptotic behavior of positive solutions for the Hénon-Lane-Emden system$ \begin{align*} \left\{ \begin{array}{l} -\Delta u = |x|^{\alpha}v^{p} \qquad\mbox{in}\; B_{1}\setminus\{0\}\subset\mathbb{R}^{N}\\ -\Delta v = |x|^{\beta}u^{q} \qquad\mbox{in}\; B_{1}\setminus\{0\}\subset\mathbb{R}^{N} \end{array} \right. \end{align*} $with an isolated singularity. The parameters $ \alpha, \beta\leq0 $ are constrained by $ \alpha+\beta>-4 $, $ p, q\geq1 $ and $ B_1 $ is the unit ball centered at the origin in $ \mathbb{R}^N $ with $ N\geq4 $. We establish results concerning the existence, regularity, upper and lower bounds estimates of positive solutions, which generalize a series of conclusions in Soranzo (1997) for the corresponding biharmonic equation (i.e. $ \alpha = 0 $ and $ p = 1 $).